eprintid: 1492672
rev_number: 44
eprint_status: archive
userid: 608
dir: disk0/01/49/26/72
datestamp: 2016-05-09 16:29:30
lastmod: 2021-10-04 00:09:34
status_changed: 2016-05-10 11:55:59
type: article
metadata_visibility: show
creators_name: Li, Z
creators_name: Carroll, J
title: An analytical model of the influence of cone sensitivity and numerosity on the Rayleigh match
ispublished: pub
divisions: UCL
divisions: B04
divisions: C05
note: Copyright © 2016 Optical Society of America. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited.
abstract: The Rayleigh match is defined by the range of mixtures of red and green lights that appear the same as an
intensity-adjustable monochromatic yellow light. The perceptual match indicates that the red–green mixture
and the yellow light have evoked the same respective cone absorptions in the L- and M-cone pathways. Going beyond
the existing models, the Poisson noise in cone absorptions is proposed to make the matching proportion of
red–green mixtures span a finite range because any mixture in that range evokes cone absorptions that do not differ
from those by a yellow light by more than the variations in the absorption noise. We derive a mathematical formula
linking the match midpoint or match range with the sensitivities and numerosities of the two cones. The noise-free,
exact, matching point, close to the midpoint of the matching range, depends only on the L- and M-cone sensitivities
to each of the red, green, and yellow lights [these sensitivities, in turn, depend on the preferred wavelengths (λmax)
and optical densities of the cone pigments and the properties of prereceptoral light filtering]. Meanwhile, the matching
range depends on both these cone sensitivities and the relative numerosity of the L and M cones. The model
predicts that, in normal trichromats, all other things being equal, the match range is smallest when the ratio
r between L and M cone densities is r = R−1∕2 with R as the ratio between the sensitivities of the L and M
cones to the yellow light, i.e., when L and M cones are similarly abundant in typical cases, and, as r departs
from R−1∕2, the match range increases. For example, when one cone type is 10 times more numerous,
the match range increases two- to threefold, depending on the sensitivities of the cones. Testing these model
predictions requires either a large data set to identify the effect of one factor (e.g., cone numerosity) while averaging
out the effects of the other factors (e.g., cone sensitivities) or for all factors to be known. A corollary of this
prediction is that, because they are more likely than usual to have L:M cone ratios skewed, the matching ranges
of normal female trichromats who are carriers of dichromacy (but not anomalous trichromacy) are likely to have a
larger matching range than usual, particularly for the deutan carriers. In addition, the model predicts that, in strong
tetrachromats (whose four dimensions of color are preserved post-receptorally), either the Rayleigh matching is
impossible or the matching range is typically smaller than usual.
date: 2016-03-01
date_type: published
official_url: http://dx.doi.org/10.1364/JOSAA.33.00A228
oa_status: green
full_text_type: other
language: eng
primo: open
primo_central: open_green
verified: verified_manual
elements_id: 1121515
doi: 10.1364/JOSAA.33.00A228
lyricists_name: Li, Zhaoping
lyricists_id: ZLIXX86
actors_name: Li, Zhaoping
actors_id: ZLIXX86
actors_role: owner
full_text_status: public
publication: Journal of the Optical Society of America A
volume: 33
number: 3
pagerange: A228-A237
issn: 1084-7529
citation:        Li, Z;    Carroll, J;      (2016)    An analytical model of the influence of cone sensitivity and numerosity on the Rayleigh match.                   Journal of the Optical Society of America A , 33  (3)   A228-A237.    10.1364/JOSAA.33.00A228 <https://doi.org/10.1364/JOSAA.33.00A228>.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/1492672/7/Li_JOSA_paper2016.pdf